Year: 2018
Type: preprint
Abstract: Let $\mathcal{F}$ be a family of sets in some metric space. In the $\mathcal{F}$-chasing problem, an online algorithm observes a request sequence of sets in $\mathcal{F}$ and responds (online) by giving a sequence of points in these sets. The movement cost is the distance between consecutive such points. The competitive ratio is the worst case ratio (over request sequences) between the total movement of the online algorithm and the smallest movement one could have achieved by knowing in advance the request sequence. The family $\mathcal{F}$ is said to be chaseable if there exists an online algorithm with finite competitive ratio. In 1991, Linial and Friedman conjectured that the family of convex sets in Euclidean space is chaseable. We prove this conjecture.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: TRIPODS: Algorithms for Data Science: Complexity, Scalability, and Robustness., CAREER: The Interplay between Combinatorial Optimization and Algorithmic Convex Geometry, TRIPODS+X: RES: Collaborative Research: Scaling Up Descriptive Epidemiology and Metabolic Network Models via Faster Sampling
OpenAlex ID: W4289306419